Of course, crossfit is only one source of instruction.
The emphasis really is on the "cross." I was a fat slug (and I am once again, I got sick). They were good folk and they let me do what I wanted and what I could. I was amazed after a few months what I could do.
I don't think it makes sense to do one or two things exclusively, we have a lot of muscles that do complicated things. Crossfit makes sense and it worked for me.
http://games2010.crossfit.com/static/images/megan_glassmanin...
I recommend starting with a favorite CrossFit exercise: kipping pull-ups. They're a great way to rid yourself of unwanted arm mobility.
After you've gotten your elbows in top shape with kipping pull-ups, I recommend focusing on the CrossFit kettlebell swing (AKA American swing, not to be confused with the hard-style swing). This exercise is so cutting edge that it has yet to be recommended by any competitive kettlebell lifters (girevoy sport) or their coaches. Interestingly, some of these aforementioned people are critical of the CrossFit swing, but I assume this is because they're Russians and Easter Europeans who lack an appreciation for the kind of think-outside-the-box innovation that comes natural to American entrepreneurs such as Glassman.
Try it out, but don't buy into any faddish aspect and don't overdo it.
If you'd like to see maximal strength/muscle gains, go see a powerlifting/olympic lifting coach for a few sessions (or join their likely weekly program for not very much $$) and do a linear progression program like Greyskull, Starting Strength, etc.
"but what about my core?" Guess what? After years of squatting on medicine balls packed to the ceiling, I can't say I had a strong core. Squat 2+x your body weight and you'll be surprised how magically strong your core gets :-)
If you are trying to lose weight, I would mainly focus on weight training. I would also add in walking, swimming, running, or biking.
Diet wise: more protein rich food, more fruits and veggies, and cut out high-fructose corn syrup/high sugar products. Eating healthy is just as important as the exercise itself.